Perfect Solar Absorber Based on Four-Step Stacked Metamaterial

Abstract

Solar absorbers are of great significance in the development of new energy technologies. However, the current approaches are mostly complex and fail to achieve high absorption rates across a wide range of wavelengths. Here, we propose a four-step stacked metamaterial solar absorber that achieves near-perfect absorption. Our four-step stacked absorber (FSSA) boasts an average absorption rate of 96.32% from 499 nm to 2348.3 nm, and a high average absorption rate of 94.96% from 300 nm to 2500 nm. Electromagnetic mode analysis and the impedance matching theory were employed to analyze the designed FSSA, which revealed that the high absorption rates are due to the propagating surface plasmon resonance (PSPR) and localized surface plasmon resonance (LSPR) modes. The FSSA offers broadband, high absorption rates, and high spectrum selectivity. Additionally, the structural parameters are adjusted to optimize the proposed perfect solar absorber. This proposed absorber can have promising applications in the renewable energy industry.

1. Introduction

With the evolution of technology, the issue of energy scarcity has become increasingly apparent [1]. As a result, there has been a growing focus on the effective extraction and utilization of solar energy [2,3,4]. It is crucial to utilize the 300–2500 nm band to its full potential, as the solar radiation spectra of the AM1.5 shows that energy is concentrated in the ultraviolet, visible light, and infrared range. Solar absorbers have proven to be more efficient and have a broader bandwidth than solar cells and thermal power generation [5,6].

Metamaterials, which are artificially created materials with unique properties [7,8,9,10,11], have been introduced into absorbers since 2008 [12]. The fundamental idea behind metamaterials is to create micro–nano structures based on already-existing materials and then reorganize them periodically to create new materials with novel properties [13,14,15,16,17]. These materials have the potential to increase the bandwidth and effectiveness of absorbers, and are frequently used in metal–insulator–metal (MIM) frameworks with complicated patterns and multilayer stacked structures to excite plasmonic resonances and provide broadband absorption [18,19,20,21,22,23,24].

The MIM structures are usually designed as a combination of a metallic substrate, a dielectric spacer and a top patterned metallic layer with resonators. Metal resonators of varying sizes are arranged horizontally, with multiple resonators overlaid to achieve broadband absorption. Recently, Yu et al. utilized a W-SiO₂-Au structure and incorporated Ti cylinders and rectangular parallelepipeds above W to create a resonator that achieved absorption greater than 90% within the range of 166.8–1926.6 nm, with an average absorption of 93.17% [25]. While using the precious metal gold, this approach does not produce high absorption. Zhu et al. also reported a Ti-Al₂O₃-Ti structure and etched a four-arrow pattern on the top layer of Ti, resulting in an average absorption of 95.21% within the range of 300–2000 nm [26]. Unfortunately, this approach uses extremely complicated patterns with a minimal parameter accuracy of 15 nm on the top layer and has stringent process requirements. Tang et al. introduced a cross-shaped Ti absorber that achieved an average absorption of 97% within the range of 386–1178 nm [27]. Despite great success in building absorbers with horizontally structures, a bottleneck issue, often overlooked in previous studies, is how to simplify the design and manufacturing processes. Compared with complex pattern structures, multi-layer stacked structures have more significant design and implementation advantages. Recently, Wu et al. designed a W-SiO₂ overlapped nanoporous structure, achieving an average absorption of 98.9% at 260–1580 nm, as well as insensitive to the polarization angle of incident light [28]. Although this structure has a high absorption rate, the W layer on the substrate has a thickness of 1 um, and there are up to 15 stacked layers of W-SiO₂. Liu et al. devised a cross-shaped fractal Fe-Si multilayer structure with an average absorption of 91% at 400–2000 nm [29]. The structure is complex and utilizes precious metals such as gold, which increases manufacturing costs but fails to achieve high absorption and good spectral selectivity.

Therefore, how to design an ultra-broadband, high-spectral-selectivity, and high-efficiency absorber is a problem yet to be settled. In this paper, we propose a four-step stacked ultra-broadband absorber based on the MIM structure of Ni-SiO₂ in the solar spectrum. The problem of high costs can be efficiently solved by using nickel, which has significantly more deposits on Earth than more conventional metals like gold and silver. Ultimately, we not only purposefully avoided complex patterns in the design, but also achieved an average absorption of 96.32% in the wavelength range of 499–2348.3 nm. From 300 nm to 2500 nm, the average absorption was 94.96%. Broadband and high absorption generation is driven by the combination of localized surface plasmon resonance (LSPR) and propagating surface plasmon resonance (PSPR) modes. The developed structural model can guarantee the polarization independence of light at vertical incidence since it is geometrically symmetric towards the x-axis and y-axis. Under various polarization modes, the incident angle can be varied. When the incident angle changes between 0 and 60 degrees in the TE mode, the absorption spectrum does not change considerably; when the incident angle changes between 0 and 50 degrees in the TM mode, the absorption spectrum does not shift significantly.

2. Structure Design and Simulation

The four-step stacked absorber (FSSA) is illustrated in Figure 1. The Ni-SiO₂ combination used in this design creates a four-step, extremely symmetrical periodic structure. For the simulation, the data for the materials were taken from Palik [30]. We chose the period P to be 500 nm. The lengths of the square steps were x₁ = 400 nm, x₂ = 300 nm and x₃ = 200 nm, respectively. Additionally, nickel with a depth of 200 nm, which is substantially greater than its skin depth, was chosen as the substrate because it can block nearly all transmissions and cause the absorption (A) to meet the equation A = 1 − R. The thickness of each layer (Ni-SiO₂) is 40 nm.

In this study, the optical characteristics and electromagnetic field analysis are determined numerically using the finite difference time domain (FDTD) method. We set the x and y directions as periodic boundary conditions after modeling the structure as a single period, and the z direction as a perfectly matched layer (PML). The incident light has a wavelength of 300–3000 nm and is directed downward vertically. Monitors were set up for data gathering, and the mesh size of simulation area was 5 nm × 5 nm × 5 nm.

3. Results and Discussion

In Figure 1b, the red line shows absorption of the absorber. The results of a comparison of the normalized solar radiation spectrum at the same time revealed that it featured good spectral selectivity. In the wavelength range of 499–2348.3 nm, with an average absorption of 96.32%. At 300–2500 nm, the average absorption is 94.96%.

In addition to the average absorption, the mid-infrared band solar absorption efficiency $\alpha$ and energy emissivity $\mathsf{\epsilon }$ can both be used to describe the properties of solar absorber. The formulas for calculating $\alpha$ and $\mathsf{\epsilon }$ can be expressed as

$$\alpha =\frac{{\int }_{280\mathrm{n}\mathrm{m}}^{2500\mathrm{n}\mathrm{m}}{I}_{AM1.5}\left(\lambda \right)A\left(\lambda \right)\mathrm{d}\lambda }{{\int }_{280\mathrm{n}\mathrm{m}}^{2500\mathrm{n}\mathrm{m}}{I}_{AM1.5}\left(\lambda \right)\mathrm{d}\lambda }$$

(1)

$$\mathsf{\epsilon }=\frac{{\int }_{2500\mathrm{n}\mathrm{m}}^{20000\mathrm{n}\mathrm{m}}{I}_B\left(\lambda ,T\right)A\left(\lambda \right)\mathrm{d}\lambda }{{\int }_{2500\mathrm{n}\mathrm{m}}^{20000\mathrm{n}\mathrm{m}}{I}_B\left(\lambda ,T\right)\mathrm{d}\lambda }$$

(2)

where $I_{AM1.5}\left(\lambda \right)$ indicates the solar radiation spectrum under the assumption of atmospheric mass 1.5. $I_B\left(\lambda ,T\right)$ is the ideal black body radiation energy spectral density. $I_B\left(\lambda ,T\right)$ is defined as follows, where h denotes the Planck constant, k is the Boltzmann constant and c indicates the velocity of light in a vacuum.

$$I_B\left(\lambda ,T\right)=\frac{2h{c}^2}{{\lambda }^5\left(e^{hc∕\lambda kT}-1\right)}$$

(3)

The integral range of the calculation formula was chosen from 280 nm to 2500 nm and the integral range of the energy emissivity in the mid-infrared band was chosen from 2500 nm to 20,000 nm because the majority of the energy in sunlight is focused in the ultraviolet-to-near-infrared band. The computed findings reveal that the suggested FSSA performs very well, with a solar absorption efficiency of 95.1% and an energy emission rate of 3.5% at 300 K.

Figure 2a shows that the dielectric layer is necessary for the absorption performance, and when the dielectric layer is removed, the absorption performance is significantly worse. We were able to effectively stimulate three peaks at 787.5 nm, 994.8 nm and 1675 nm with peaks of 99.8%, 98.3% and 98.2%, respectively, by the interaction of the metal medium.

Figure 2b displays the normalized xoz and yoz plane electric field intensity distributions, where x and y represent the horizontal and vertical dimensions of the unit cell, respectively. This information is provided to help further understand the broadband absorption mechanism.

Localized surface plasmons are excited at the metal–dielectric interface at each step, as can be seen in Figure 3a. The Slowlight Waveguide Mode (SWM), which causes the light focused in the structure to be lost and minimizes reflection, is produced by the weakly coupled resonance effect that is stimulated by the anisotropy of the stairs generated by the alternating metal–dielectric [31].

Figure 3b displays the normalized electric field intensity distribution at each step of the interface at the three peaks, and each layer stimulates localized surface plasmon resonance (LSPR) at three peaks from the perspective of the lateral electric field distribution, whereas, from the perspective of the longitudinal electric field distribution, the incident light is captured by the top region of the stepped structure at short wavelength vertical incidence, and the magnetic resonance is concentrated in the top part of the nanostructure, which is primarily the result of the combined effect of propagating surface plasmon resonance (PSPR) and LSPR. As shown in Figure 3c, as the number of layers increases, the absorption spectrum first increases and then decreases, reaching its maximum at four layers.

Additionally, the second-layer step magnetic resonance is strengthened at a wavelength of 787.5 nm. The downward shift of the magnetic resonance is more noticeable at wavelengths of 994.8 nm and below, until the 1675 nm completely occurs at the second step and appears at the third step. This is due to the fact that Ni and SiO₂ exhibit metal and dielectric properties in the solar spectrum region; the nearby Ni-SiO₂-Ni structure is a MIM structure, which allows the electric field to be diffused over the nearby composite layers as well. Each layer’s breadth steadily rises in the structural parameters, and the width of each layer is strongly correlated with the plasma excitation wavelength. Because different composite layers correlate to various plasmonic excitation wavelengths, there will be a modest downward shift in the energy distribution as the wavelength rises. Thus, broadband absorption is possible.

In order to monitor the absorption while adjusting the structural parameters using the control variable approach, we took into account the impact of structural parameters on the peak value of the absorption curve. The results are displayed in Figure 4. The ideal value of 40 nm is directly used here since changing h₂ would significantly affect the total absorption impact. The three peaks are all directly influenced by the size of h₂, which has a direct impact on the composite layer’s capacity to localize the electromagnetic field. The absorption changes by 2% for each color change in Figure 4, where the darkest area corresponds to an absorptivity of more than 98%.

Prior to studying the parameter P, we fixed other parameters. The simulation was run with a 20 nm step size between 460 nm and 540 nm. Figure 4a presents the findings. As can be observed, as the period P shifts from 460 nm to 540 nm, the wavelength of more than 90% absorptivity progressively lowers. However, two peaks are simultaneously stimulated at 490nm, and the peak breadth marginally rises as the period increases. Although the effective absorption bandwidth rises at 460 nm, the average absorption and spectral selectivity both decline. The average absorption rises at 540 nm, but the actual absorption bandwidth falls. The coupling theory between nearby unit structures may be used to explain this occurrence, and by varying the size of P, the coupling capacity of the structures between adjacent units can be changed. The ultimate P value is 500 nm when the absorption bandwidth and average absorption efficiency are taken into account.

Second, the absorption varies as seen in Figure 4b when the parameter x₁ is changed. The first peak range remains essentially unaltered as x₁ shifts from 360 nm to 440 nm, the second peak range vanishes when x₁ exceeds 400 nm, and the absorption range dramatically shrinks by more than 96% when x₁ exceeds 420 nm. The overall stepped structure is destroyed by the increased width of x₁, making it challenging to excite long-wavelength plasmons. Similarly, x₁ is chosen to be 400 nm in order to balance the effective absorption bandwidth and the average absorption efficiency.

Figure 4c depicts the same absorption curve where the value of x₂ is the sole variable changed. At 260 nm and 340 nm, the effective absorption bandwidth of x₂ essentially remains the same, although the range above 96% varies substantially. The band above 96% is tiny at 260 nm, and the absorption range greater than 96% reaches its maximum at 300 nm, before progressively declining beyond 340 nm. It is important to note that the first peak’s range is at its greatest when x₂ is 280 nm and gradually gets smaller as x₂ increases, while the second peak cannot be aroused at this time. The absorption range over 96% reaches its maximum only when x₂ takes 300 nm, causing the two peaks to coexist.

Figure 4d displays the absorption spectra that result from changing the x₃ parameter. Similar to x₂, changing x₃ has major implications on the excitation and width of the second peak but has little impact on the effective absorption bandwidth. When x₃ is changed from 160 nm to 240 nm, the bandwidth corresponding to the absorption greater than 96% is maximized between 190 nm and 210 nm. At 200 nm, the first peak is the widest and the second peak can be maintained, whereas at 210 nm, the first peak is slightly narrower and the second peak is the widest. As a result, the parameter x₃ can be employed with either 200 nm or 210 nm, and its absorption performance is outstanding. To guarantee the width of the first peak initially, x₃ is chosen to be 200 nm because the energy of the sun spectrum is primarily distributed at short wavelengths. Collectively, P and x₃ have the greatest influence on the first peak’s excitation and width, respectively. The second peak’s excitation is governed by a combination of four parameters; x₂ determines location, and x₃ regulates width.

Impedance matching theory is used to investigate the proposed FSSA absorption mechanism in addition to the electromagnetic mode analysis. Theoretically, it has been established that the metamaterial structure qualifies as an effective homogeneous medium, and that effective permittivity ε and effective permeability μ may be used to describe its characteristics. By altering the geometry, material properties, and structure of the metamaterial, the two parameters can be changed. The metamaterial absorber may accomplish impedance matching with free space in the solar spectrum region, minimize reflection loss, and achieve high absorption through the regulation of ε and μ.

$$\left|Z\left(\lambda \right)\right|=\frac{\mathrm{u}\left(\lambda \right)}{\mathsf{\epsilon }\left(\lambda \right)}=\sqrt{\frac{{\left(1+S_{11}\right)}^2-S_{21}^2}{{\left(1-S_{11}\right)}^2-S_{21}^2}}$$

(4)

$$\mathrm{R}\left(\lambda \right)=\left|\frac{Z\left(\lambda \right)-Z_0}{Z\left(\lambda \right)+Z_0}\right|$$

(5)

In the formula, $Z_0=\sqrt{\frac{{\mathrm{u}}_0}{{\mathsf{\epsilon }}_0}}=1$ is the free space impedance, and S₁₁ and S₂₁ have a square relationship with the reflection coefficient and transmission coefficient, respectively. Using the aforesaid method, we estimated the FFSA impedance matching. Figure 5a demonstrates that, for the calculated solar spectrum band, the impedance value remains extremely close to 1.

In order to further demonstrate the excellent performance of FSSA, it is necessary to demonstrate its insensitivity to polarization angle and incident angle, because in the context of a practical application scenario for solar absorbers, the incident angle and polarization angle of sunlight are random. The findings of the initial scan, which covered the polarization angle range of 0–90°, are displayed in Figure 5b. The electromagnetic responses to incident light at all polarization angles are essentially the same in FSSA due to its straightforward structure and high degree of symmetry, hence the absorption spectra does not vary when the polarization angle fluctuates.

As is apparent in Figure 5c,d, FSSA absorption spectra with an incidence angle spanning from 0° to 60° could be observed when TE and TM waves were incident. The absorption line is almost stable between 0° and 50° of incident angle under the incidence of TE waves, and it slightly decreases at 60°, but it may still guarantee an average absorption of more than 90% in the solar spectrum range.

FSSA is more sensitive to the incidence angle of the TM wave than the TE wave. When the incidence angle is between 0° and 40°, the average absorptivity under TM circumstances is better than 90%; at 50°, it can be maintained at more than 85%; at 60°, it can only preserve around 80%, but the performance is still outstanding.

Figure 6 depicts three schemes with different materials. Fe is a widely available, inexpensive metal that is used frequently [32,33]. It was discovered that employing Fe as the material allowed for the maintenance of an absorption effect of more than 90% from 493 nm to 2299.4 nm, and an average absorption of 95.28% from 300 nm to 2500 nm. It is only used, though, when cost is a concern, because it is neither corrosion- or high-temperature-resistant, which makes air-contacting parts more likely to oxidize and lose performance stability after actually being manufactured.

Due to the imaginary portion of its dielectric constant, Ti can readily produce strong plasma resonance and produce large losses. Recently, Ti has been widely employed in the field of solar absorbers, due to its great temperature resistance. Ti and Al₂O₃ in this structure may sustain an absorption effect of more than 90% at 503.5–2633 nm and an average absorption of 94.68% at 300–3000 nm.

Although the Ti absorber has excellent performance and great stability, we introduced nickel (Ni) material to further reduce costs. Ni is a ferromagnetic metal with superior corrosion resistance, high temperature resistance, oxidation resistance, and strong ductility. The price of Ni is less than that of other widely used metals like Ti and Au [34,35].

We utilized Ti as additional basic materials for parameter control as a supplement to Ni. The outcomes are displayed in Figure 7. It is evident from the figure that, by using the scheme P-x₁-x₂-x₃ is 500-400-300-200 nm, an excellent absorption effect can be obtained. The changes in the absorption curves of Ti with parameter changes are essentially the same as those of Ni, but due to the influence of the metal’s intrinsic properties, the specific absorption bandwidth and absorption efficiency are slightly different. It can, however, be further tailored to certain materials. The Fe scheme, for instance, can employ 520-380-300-210 nm, and the Ti scheme, 510-390-320-210 nm.

In conclusion, by correctly modifying the geometric parameters of the nanostructures for the material scheme, the absorption performance of the developed ultra-broadband absorber may be further enhanced, offering greater flexibility for practical applications. The parameters we chose are also rather conservative, balancing the absorption rate and absorption bandwidth, so an inaccuracy in any one of them within a 5 nm range will not have a substantial influence on the absorption effect, giving us some leeway in the actual process of preparation.

We analyzed the excellent performance of FSSA and compared it with recently published papers, as shown in

Table 1. Performance comparison to other absorbers (/ means that the data is not explicitly stated in the study).

Ref.	Material	Multi-Layer Stacking	Number of Layers	Complex Pattern	Wavelength (A > 90%)	Average Absorption
[25]	Au/SiO2/W/Ti	No	/	Titanium resonator	167–1926 nm	93.17%
[27]	TiN/SiO2/Ti	No	/	cross-shaped	386–1178 nm	95%
[29]	Au/Si/Fe	Yes	4	cross-shaped fractal	400–2000 nm	96.67%
[36]	TiN/SiO2/TiO2	No	/	ellipse	360–1624 nm	95.68%
[37]	Ti/W/SiO2/Ni	Yes	15	/	300–1909 nm	96%
[38]	Fe/Si	Yes	18	/	300–3000 nm	96%
proposed	Ni/SiO2	Yes	8	/	499–2348 nm (300–2500 nm)	96.32% (94.96%)

. Both MIM absorbers with a horizontal structure and those with a vertical structure make up the majority of the types in the table. For the horizontal structure, which corresponds to Refs. [25,27,36] in the table, the multi-level resonance is primarily excited by the top pattern, but the complexity of the top pattern has a significant impact on the horizontal structure’s absorption bandwidth, increasing the fabrication process’s difficulty. While Ref. [29] contains both vertical and horizontal structures, it is also challenging to produce despite its high performance. Additionally, two vertical structure absorbers with 15 and 18 layers, respectively, and extraordinarily high thickness and density of layers, are listed in Ref. [37] and Ref. [38]. Despite having better performance, the actual manufacturing is pricey.

The proposed structure offers the advantage of high absorption while keeping a wider bandwidth, as can be obtained from the table. The FSSA offers high performance in the solar spectrum while using inexpensive materials, avoiding complicated patterns and multi-layer stacking, and has significant practical utility.

4. Conclusions

In this research, the FDTD method was used to obtain the absorption of the solar absorber. The proposed FSSA, which is based on the MIM structure, achieves an average absorption of 96.32% in the range of 499–2348 nm, and in the range of 300–2500 nm achieves 94.96% by using Ni as the primary material, which is corrosion-resistant, high-temperature-resistant, and inexpensive. Contrary to the absorber that has been proposed, FSSA is straightforward, avoiding complex patterns and multi-layer stacking. Layer height is uniformly 40 nm after parameter optimization, and the rest of the parameters are multiples of 100 nm, greatly reducing the requirements for the manufacture process. Additionally, the suggested structure may further boost the absorption and bandwidth by altering the material in addition to fine-tuning the bandwidth by tweaking the parameters. In conclusion, FSSA is a very effective absorber that was created for the solar spectrum, and it has a significant amount of potential for the renewable energy industry.